Harvard Professor E.O Wilson sparked an interesting debate on the Wall Street Journal on the role of mathematics in scientific thinking. A small excerpt:

For many young people who aspire to be scientists, the great bugbear is mathematics. Without advanced math, how can you do serious work in the sciences? Well, I have a professional secret to share: Many of the most successful scientists in the world today are mathematically no more than semiliterate.

The most important skill is the ability to form concepts, not math:

Fortunately, exceptional mathematical fluency is required in only a few disciplines, such as particle physics, astrophysics and information theory. Far more important throughout the rest of science is the ability to form concepts, during which the researcher conjures images and processes by intuition.

.. Pioneers in science only rarely make discoveries by extracting ideas from pure mathematics. (..) Real progress comes in the field writing notes, at the office amid a litter of doodled paper, in the hallway struggling to explain something to a friend, or eating lunch alone.

The question here is an important one: does our ability to form complex concepts develop before or after mathematical modeling? Prof. Wilson seems to suggest that great ideas come first (while eating lunch or in the hallway etc.) and then mathematical models give structure to your thinking. But most scholars have an opposite view. Paul Krugman, for example, says that his ability to develop good ideas comes after mathematical models, not before:

mathematical grinding served an essential function (…) of clarifying my thought. In the economic geography stuff, for example, I started with some vague ideas; it wasn’t until I’d managed to write down full models that the ideas came clear.

Afterthe math I was able to express most of those ideas in plain English, but it really took the math to get there, and you still can’t quite get it all without the equations.

Over at The Slate, Math professors Edward Frenkel suggests not to be math-phobic as well. He says: “Don’t listen to E.O Wilson”:

It would be fine if Wilson restricted the article to his personal experience, a career path that is obsolete for a modern student of biology. We could then discuss the real question, which is how to improve our math education and to eradicate the fear of mathematics that he is talking about. Instead, trading on that fear, Wilson gives a misinformed advice to the next generation, and in particular to future scientists, to eschew mathematics. This is not just misguided and counterproductive; coming from a leading scientist like him, it is a disgrace. Don’t follow this advice—it’s a self-extinguishing strategy.